This graph represents models covered in Farhmeier et al., though I add the Gaussian process connection beyond spatial regression. Hover over the links for details on some connections. Dots indicate ‘special cases of’ the parent node. Undirected connections suggest equivalence (≡ on hover) or a more complex relationship (usually for more general/more complex models). Note this is for a quick reference, not an exhaustive one.
The text builds up from standard regression models to additive models incorporating nonlinear effects, mixed models that can take on hierarchical and other correlation structure, and spatial models. These latter three can be arbitrarily combined in a penalized regression approach, and Farhmeier et al. refer to these as structured additive regression models. Various forms of these can be seen as Gaussian process models employing specific covariance structures. Wood’s mgcv incorporates STAR models of many kinds.
Regression: standard linear model
GLM: generalized linear model
Mixed Model: generalized linear mixed model
GAM: generalized additive models
Spatial: standard spatial regression models, e.g. kriging
STAR: structured additive regression model
GP: Gaussian process